I use R2 to shift up and L2 to shift down, or I tap reverse to shift(!!, it works if you drive it into the red, you just tap it and it makes the cluth like slip into the next gear, you can also shift down, or just tap it, then go around a corner(off the gas) and hit the gas and you are in the right gear). Sometimes, like with my slower cars(hybrids, I made several realistic cars like a Probe GT and US-spec Lancer), I'll use reverse all the time cause I like the sound of the RPMs slowing for the next gear, and you can also get an "into 2nd gear scratch" which is cool. On the fast cars, reverse slows you down(cars with several thousand HP, when you tap reverse there's power too quick and it slows you down). Only problems with reverse is that if you spin the wheels, causeing the RPMs to go up into the red, you can't shift because you aren't actually going fast enough to be in the red. Also some cars with really big red areas(like between the start of the red and the limiter), if you go right up to the limiter(with out hitting it)and tap reverse, it could shift twice if the shift from the limiter to the next gear keeps you in the red. Also if you tap reverse too early, it kicks it out of gear(on the slow cars it's pretty bad, but on the fast cars it doesn't do much)and then back in.
It's really fun to drive using reverse to shift, try it.
With other shifting, I rarely mess up, but there have been times where I'm playing, and I accidently hit the controller on the pillow or side of my bed, and it hits L2 or R2 and shifts...